Question

Which graph represents a reflection of f(x) = 2(0.4)x across the y-axis?

Answer 1

a

Step-by-step explanation:

Answer 2

Answer: The correct option is A.

Step-by-step explanation:

The given function is,

`f(x)=2(0.4)^x`

To find the graph of this function after the reflecting across y-axis, first we have to find the graph of the equation.

The value of the function is 2 when x=0, so, the graph of given equation intersect the y-axis at 2.

In the equation
`(0.4)^x`. Since
`0<0.4<1`, so the given function is decreasing function.

`f(x)\rightarrow 0 \text{ as }\rightarrow \infty`

`f(x)\rightarrow \infty \text{ as }\rightarrow -\infty`

The value of f(x) is always positive, so the graph of f(x) is always above the x-axis. Thus, the graph must be above the x-axis after reflection across y-axis.

So, the option (2) and (4) and incorrect.

When we reflect the graph across the y-axis then,

`f(x)\rightarrow \infty \text{ as }\rightarrow \infty`

`f(x)\rightarrow 0 \text{ as }\rightarrow -\infty`

It means when x approaches to large negative number the f(x) approaches to 0 and when x approaches to large positive number the f(x) approaches to infinite.

Therefore, the correct option is show in first graph.